Image-forming MR methods which utilize the interaction between magnetic fields and nuclear spins in order to form two-dimensional or three-dimensional images are widely used nowadays, notably in the field of medical diagnostics, because for imaging of soft tissue they are superior to other imaging methods in many respects, do not require ionizing radiation and are usually not invasive.
According to the MR method in general, the object, for example the body of the patient to be examined, is arranged in a strong, uniform magnetic field whose direction at the same time defines an axis (normally the z-axis) of the co-ordinate system on which the measurement is based. The magnetic field produces different energy levels for the individual nuclear spins in dependence on the magnetic field strength which can be excited (spin resonance) by application of an electromagnetic alternating field (RF field) of defined frequency (so-called Larmor frequency, or MR frequency). From a macroscopic point of view the distribution of the individual nuclear spins produces an overall magnetization which can be deflected out of the state of equilibrium by application of an electromagnetic pulse of appropriate frequency (RF pulse), so that the magnetization performs a precessional motion about the z-axis. The precessional motion describes a surface of a cone whose angle of aperture is referred to as flip angle. The magnitude of the flip angle is dependent on the strength and the duration of the applied electromagnetic pulse. In the case of a so-called 90° pulse, the spins are deflected from the z axis to the transverse plane (flip angle 90°).
After termination of the RF pulse, the magnetization relaxes back to the original state of equilibrium, in which the magnetization in the z direction is built up again with a first time constant T1 (spin lattice or longitudinal relaxation time), and the magnetization in the direction perpendicular to the z direction relaxes with a second time constant T2 (spin-spin or transverse relaxation time). The variation of the magnetization can be detected by means of receiving RF coils which are arranged and oriented within an examination volume of the MR device in such a manner that the variation of the magnetization is measured in the direction perpendicular to the z-axis. The decay of the transverse magnetization is accompanied, after application of, for example, a 90° pulse, by a transition of the nuclear spins (induced by local magnetic field inhomogeneities) from an ordered state with the same phase to a state in which all phase angles are uniformly distributed (dephasing). The dephasing can be compensated by means of a refocusing pulse (for example a 180° pulse). This produces an echo signal (spin echo) in the receiving coils.
To realize spatial resolution in the body, constant magnetic field gradients extending along the three main axes are superposed on the uniform magnetic field, leading to a linear spatial dependency of the spin resonance frequency. The signal picked up in the receiving coils then contains components of different frequencies which can be associated with different locations in the body. The signal data obtained via the receiving coils corresponds to the spatial frequency domain and is called k-space data. The k-space data usually includes multiple lines acquired with different phase encoding. Each line is digitized by collecting a number of samples. A set of k-space data is converted to a MR image by means of an image reconstruction algorithm.
MR imaging is sensitive to diffusion. Known diffusion weighted imaging (DWI) techniques are commonly performed by using imaging sequences comprising diffusion gradients, wherein the diffusion of protons (of water molecules) along the direction of the diffusion gradient reduces the amplitude of the acquired MR signals. Diffusion tensor imaging (DTI) is a more sophisticated form of DWI, which allows for the determination of both the magnitude and the directionality of diffusion. For example, DTI enables to visualize white matter fibers in MR brain imaging and can map subtle changes in the white matter associated with diseases like brain infarction, multiple sclerosis, epilepsy etc. The so-called fractional anisotropy (FA) provides information about the shape of the diffusion tensor at each voxel position of a MR image. The FA is determined from the variance of the eigenvalues of the diffusion tensor. Hence, the FA reflects differences between the isotropic and the linear diffusion at a given image position. A technique called diffusion tensor tractography (DTT) has been developed recently as a variant of DTI. This technique enables the non-invasive tracking of neuronal fibers in the brain. White matter fiber trajectories are reconstructed by tracking the direction of fastest diffusion which is assumed to correspond to the longitudinal axis of the fiber.
Brain DWI techniques are particularly vulnerable to macroscopic head motion, as the signal attenuation resulting from the motion can confound the measurement of interest. Subject motion during an MR examination can be particularly problematic in populations like children, the elderly, or patients with medical conditions that prevent them from lying still, such as Parkinson's disease. Motion affects the data in two main ways: shifts of the brain tissue to be imaged (resulting in ghosting artifacts in the reconstructed MR images), and exposure to incorrect diffusion encoding.
Retrospective motion correction methods prior to determining the diffusion tensor are widely used. A basic and common way of retrospectively correcting for motion time employs a co-registration of the diffusion-weighted MR image to a reference (unweighted) MR image and a subsequent reorientation of the diffusion gradient directions that takes into account the motion at each image position. Such operations involve spatial interpolations, and these can affect partial volume effects, the variance properties of the DWI with propagation in the diffusion tensor calculation.
To avoid significant artifacts resulting from motion, DWI data have commonly been acquired using single-shot imaging sequences, such as single-shot echo-planar imaging (EPI). However, the image quality can be low and the spatial resolution is limited in single-shot DWI. The significant geometric distortions and limited spatial resolution make it difficult to measure diffusion properties at high precision. Recent efforts have been made to address the limitations of single-shot DWI.
US 2014/0002078 A1 describes a multi-shot DWI technique (termed multiplexed sensitivity encoding—MUSE) which uses parallel acquisition and inherently corrects shot-to-shot phase variations due to motion and thus avoids ghosting artifacts. Jeong et al. (Magnetic Resonance in Medicine, volume 69 (3), pages 793-802, 2013) propose a multi-shot DWI technique using a modification of the standard SENSE algorithm commonly used for fast parallel image acquisition. The modification accounts for shot-to-shot motion-induced phase errors. This known technique is termed image reconstruction using image-space sampling functions (IRIS).
However, these techniques do not take the motion-induced incorrect diffusion encoding into account.
“Effects of motion and b-matrix correction for high resolution DTI with short-axis PROPELLER-EPI” by MURAT AKSOY proposes diffusion tensor estimated directly from the complex k space data, by solving the equation with rotation and translation matrices R and Ar from the scanner frame of reference to the patient frame of reference. The equation is solved using non-linear conjugate gradient algorithm, which is described in details in “Single-step nonlinear diffusion tensor estimation in the presence of microscopic and macroscopic motion”.